Ion and Solvent Transport in Ion‐Exchange Membranes: I . A Macrohomogeneous Mathematical Model

Verbrugge, Mark W.; Hill, Robert F.

doi:10.1149/1.2086573

Cited by 243 publications

(134 citation statements)

References 25 publications

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“…This simplification goes under various names, such as "fine capillary pore model," "uniform potential (UP) model" [33,[72][73][74][75][76][77], and also as Teorell-Meyers-Sievers (TMS) theory, though TMS theory does not include fluid flow [1,35]. In the UP model, the coefficient matrix L of Eq.…”

Section: Uniform Potential Modelmentioning

confidence: 99%

Analysis of electrolyte transport through charged nanopores

et al. 2016

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We revisit the classical problem of flow of electrolyte solutions through charged capillary nanopores or nanotubes as described by the capillary pore model (also called "space charge" theory). This theory assumes very long and thin pores and uses a one-dimensional flux-force formalism which relates fluxes (electrical current, salt flux, and fluid velocity) and driving forces (difference in electric potential, salt concentration, and pressure). We analyze the general case with overlapping electric double layers in the pore and a nonzero axial salt concentration gradient. The 3×3 matrix relating these quantities exhibits Onsager symmetry and we report a significant new simplification for the diagonal element relating axial salt flux to the gradient in chemical potential. We prove that Onsager symmetry is preserved under changes of variables, which we illustrate by transformation to a different flux-force matrix given by Gross and Osterle [J. Chem. Phys. 49, 228 (1968)]. The capillary pore model is well suited to describe the nonlinear response of charged membranes or nanofluidic devices for electrokinetic energy conversion and water desalination, as long as the transverse ion profiles remain in local quasiequilibrium. As an example, we evaluate electrical power production from a salt concentration difference by reverse electrodialysis, using an efficiency versus power diagram. We show that since the capillary pore model allows for axial gradients in salt concentration, partial loops in current, salt flux, or fluid flow can develop in the pore. Predictions for macroscopic transport properties using a reduced model, where the potential and concentration are assumed to be invariant with radial coordinate ("uniform potential" or "fine capillary pore" model), are close to results of the full model.

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Section: Uniform Potential Modelmentioning

confidence: 99%

Analysis of electrolyte transport through charged nanopores

et al. 2016

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“…D eff i is effective diffusion coefficient, which is derived from the free-space value, D i , by a Bruggemann correction [20]:…”

Section: Governing Equationsmentioning

confidence: 99%

“…eff s is the effective electronic conductivity of the porous electrode, which is related to the electronic conductivity of solid material, s , subject to a Bruggemann correction [20]:…”

Section: Governing Equationsmentioning

confidence: 99%

A three-dimensional model for negative half cell of the vanadium redox flow battery

Zhang

Xing

2011

Electrochimica Acta

175

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“…Verbrugge and Hill [5,6] developed a one-dimensional model for the proton exchange membrane (MEA) based on the Nernst-Plank equation. Bernardi and Verbrugge [7] employed gas-phase transport and membrane models to investigate the performance of a gas-fed porous cathode bonded to a polymer electrolyte, and later they developed a one-dimensional isothermal model for the cell [8].…”

Section: Introductionmentioning

confidence: 99%

Effects of porosity change of gas diffuser on performance of proton exchange membrane fuel cell

Chu

Yeh

Chen

2003

Journal of Power Sources

163

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An investigation is made of the effects of the change of the porosity of the gas diffuser layer (GDL) on the performance of a proton exchange membrane (PEM) fuel cell. The analysis of fuel cell performance with non-uniform porosity of GDL is a necessity because the presence of liquid water in the GDL leads to a non-uniformly distributed porosity in the GDL. To implement this performance analysis, a half-cell model which considers the oxygen mass fraction distribution in the gas channel, the GDL and the catalyst layer, and the current density and the membrane phase potential in the catalyst layer and the membrane is investigated. Four continuous functions of position are employed to describe the porosity, and differential equations are derived based on oxygen transportation and Ohm's law for proton migration and solved numerically. Results show that a fuel cell embedded with a GDL with a larger averaged porosity will consume a greater amount of oxygen, so that a higher current density is generated and a better fuel cell performance is obtained. This explains partly why fuel cell performance deteriorates significantly as the cathode is flooded with water (i.e. to give a lower effective porosity in the GDL). In terms of the system performance, a change in GDL porosity has virtually no influence on the level of polarization when the current density is medium or lower, but exerts a significant influence when the current density is high. This finding supports the scenario proposed by previous studies that the polarization at high current density corresponds mainly to mass transfer through (or the concentration activation of) the membrane assembly.

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Ion and Solvent Transport in Ion‐Exchange Membranes: I . A Macrohomogeneous Mathematical Model

Cited by 243 publications

References 25 publications

Analysis of electrolyte transport through charged nanopores

Analysis of electrolyte transport through charged nanopores

A three-dimensional model for negative half cell of the vanadium redox flow battery

Effects of porosity change of gas diffuser on performance of proton exchange membrane fuel cell

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